How to connect a cylinder/sphere to a flat/curved surface surface?
There are many ways to do so. But the question is often, is it necessary. Something artist needs the normals of the meshes to behave appropriately and sometimes the effort just don't really pay for the little returns.

On this video the user is creating an emboss effect on a gold bar. There is alot of times he needs to be joining faces in his video. Link below.

https://www.youtube.com/watch?v=O0mkoMkEbc0

Although this maybe about embossing text the underlying method of how to join meshes pretty much applies for all cases.


Select the edges you want to fill.
Subdivide the edge with the lower vertex count to make a closer match the number of vertices.
Press AltF to fill.